Problem 33
An electron in excited hydrogen atom falls from fifth energy level to second energy level. In which of the following regions, the spectrum line will be observed and is part of which series of the atomic spectrum? (a) Visible, Balmer (b) Ultraviolet, Lyman (c) Infrared, Paschen (d) Infrared, Brackett
Problem 35
The frequency of radiation absorbed or emitted when transition, occurs between two stationary states with energies \(E_{1}\) (lower) and \(E_{2}\) (higher) is given by (a) \(\mathrm{u}=\frac{E_{1}+E_{2}}{h}\) (b) \(\mathrm{v}=\frac{E_{1}-E_{2}}{h}\) (c) \(\quad v=\frac{E_{1} \times E_{2}}{h}\) (d) \(u=\frac{E_{2}-E_{1}}{h}\)
Problem 36
The angular momentum of an electron in a given stationary state can be expressed as \(m_{e} v r=n \frac{h}{2 \pi}\). Based on this expression an electron can move only in those orbits for which its angular momentum is (a) equal to \(n\) (b) integral multiple of \(\frac{h}{2 \pi}\) (c) multiple of \(n\) (d) equal to \(\frac{h}{2 \pi}\) only.
Problem 37
According to Bohr's theory, the angular momentum of an electron in \(5^{\text {th }}\) orbit is (a) \(\frac{10 h}{\pi}\) (b) \(\frac{25 h}{\pi}\) (c) \(\frac{1.5 h}{\pi}\) (d) \(\frac{2.5 h}{\pi}\)
Problem 38
The radius of the stationary state which is also called Bohr radius is given by the expression \(r_{n}=n^{2} a_{0}\) where the value of \(a_{0}\) is (a) \(52.9 \mathrm{pm}\) (b) \(5.29 \mathrm{pm}\) (c) \(529 \mathrm{pm}\) (d) \(0.529 \mathrm{pm}\)
Problem 39
If the radius of first Bohr orbit is \(x \mathrm{pm}\), then the radius of the third orbit would be (a) \((3 \times x) \mathrm{pm}\) (b) \((6 \times x) \mathrm{pm}\) (c) \(\left(\frac{1}{2} \times x\right) \mathrm{pm}\) (d) \((9 \times x) \mathrm{pm}\)
Problem 40
What does the negative electronic energy (negative sign for all values of energy) for hydrogen atom means? (a) The energy of an electron in the atom is lower than the energy of a free electron at rest which is taken as zero. (b) When the electron is free from the influence of nucleus it has a negative value which becomes more negative. (c) When the electron is attracted by the nucleus the energy is absorbed which means a negative value. (d) Energy is released by hydrogen atom in ground state.
Problem 41
The energy of the electron in a hydrogen atom has a negative sign for all possible orbits because (a) when the electron is attracted by the nucleus and is present in orbit \(n\), the energy is emitted and its energy is lowered. (b) when the electron is attracted by the nucleus and is present in orbit \(n\), the energy is absorbed and its energy is increased. (c) when the electron is repelled by the nucleus, the energy is released and its energy is lowered. (d) None of these.
Problem 43
Bohr's theory can also be applied to the ions like (a) \(\mathrm{He}^{+}\) (b) \(\mathrm{Li}^{2+}\) (c) \(\mathrm{Be}^{3+}\) (d) all of these.
Problem 45
The Bohr's energy of a stationary state of hydrogen atom is given as \(E_{n}=\frac{-2 \pi^{2} m e^{4}}{n^{2} h^{2}}\). Putting the values of \(m\) and \(e\) for \(n^{\text {th }}\) energy level which is not the correct value? (a) \(E_{n}=\frac{-21.8 \times 10^{-19}}{n^{2}} \mathrm{~J}\) atom \(^{-1}\). (b) \(E_{n}=\frac{-13.6}{n^{2}} \mathrm{eV}\) atom \(^{-1}\) (c) \(E_{n}=\frac{-1312}{n^{2}} \mathrm{~kJ} \mathrm{~mol}^{-1}\) (d) \(E_{n}=\frac{-12.8 \times 10^{-19}}{n^{2}}\) erg \(\mathrm{atom}^{-1}\)
